The Least Squares Regression Line

The problem with drawing line of best fit by eye is that the line drawn will vary from person to person. Instead, use linear regression – Yipee!

The Least Square Regression Line For any line drawn, we can find vertical distances: d 1, d 2, d 3, … between each point on the line. Then, square each distance. Find their sum. The least square regression line is the line that makes the sum as small as possible.

The Least Square Regression Line Why would you do this by hand? USE A CALCULATOR! EXAMPLE:

TI-84+ Directions for Least Squares Regression Line

Interpolation and Extrapolation

See scatter diagram below: The data with the lowest and highest values of x are called the poles. If we use values of x in between the poles, we say we are interpolating between the poles. If we use values of x outside the poles, we say we are extrapolating outside the poles.

Accuracy The accuracy of an interpolation depends on how linear the original data was. This can be gauged by determining the correlation coefficient (r) and ensuring that the data is randomly scattered around the linear regression line. The accuracy of an extrapolation depends not only on how linear the original data was, but also on the assumption that the linear trend will continue past the poles. As a general rule, it is reasonable to interpolate between the poles, but unreliable to extrapolate outside the poles.